Projection-based reduced-order models (ROMs) play a crucial role in simplifying the complex dynamics of fluid systems. Such models are achieved by projecting the Navier-Stokes equations onto a lower-dimensional subspace while preserving essential dynamics. However, this approach requires prior knowledge of the underlying high-fidelity model, limiting its effectiveness when applied to black-box data. This article introduces a novel, non-intrusive, data-driven method–Greedy Identification of Latent Dynamics (GILD)–for constructing parametric fluid ROMs. Unlike traditional methods, GILD constructs models directly from data, without relying on specific high-fidelity model information. It also employs interpolation within the manifold R∗N×q/Oq to accommodate parameter variability. Numerical experiments on various fluid dynamics scenarios, including lid-driven cavity flow, flow past a cylinder with varying Reynolds number, and Ahmed body flow with variable geometry, demonstrate GILD’s robust performance across both training and unseen parameter values. GILD’s ability to accurately capture system dynamics and its adaptability to diverse data sources highlight its potential as a powerful tool for constructing parametric reduced-order models in an easy and general way for complex fluid dynamics and beyond.

中文翻译：

---

从参数流数据中贪婪地识别潜在动态


基于投影的降阶模型 （ROM） 在简化流体系统的复杂动力学方面发挥着至关重要的作用。这种模型是通过将 Navier-Stokes 方程投影到低维子空间上来实现的，同时保留了基本的动力学。但是，这种方法需要底层高保真模型的先验知识，因此在应用于黑盒数据时的有效性受到限制。本文介绍了一种新颖的、非侵入性的、数据驱动的方法 – 潜在动力学的贪婪识别 （GILD） – 用于构建参数化流体 ROM。与传统方法不同，GILD 直接从数据构建模型，而不依赖于特定的高保真模型信息。它还在歧管 R∗N×q/Oq 中采用插值来适应参数变化。对各种流体动力学场景的数值实验，包括盖子驱动的腔流、流经具有不同雷诺数的圆柱体以及具有可变几何形状的 Ahmed 体流，证明了 GILD 在训练和不可见参数值方面的稳健性能。GILD 准确捕获系统动力学的能力及其对不同数据源的适应性凸显了它作为强大工具的潜力，可以以简单而通用的方式为复杂的流体动力学及其他领域构建参数化降阶模型。